The analytic approximation is obtained for the Wigner distribution function which describes the thermodynamic equilibrium state in the three-dimensional space. This approximation gives the exact result for the anisotropic harmonic oscillator and has the correct quasi-classical asymptotic behaviour for an arbitrary potential. The iterative procedure is given to solve the Bloch equation for the Wigner function.
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Univ Tokyo, Inst Engn Innovat, Tokyo 1138656, JapanUniv Tokyo, Inst Engn Innovat, Tokyo 1138656, Japan
Tohei, Tetsuya
Lee, Hak-Sung
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Univ Tokyo, Inst Engn Innovat, Tokyo 1138656, Japan
Korea Inst Mat Sci, Mat Modeling & Characterizat, Chang Won 641831, South KoreaUniv Tokyo, Inst Engn Innovat, Tokyo 1138656, Japan
Lee, Hak-Sung
Ikuhara, Yuichi
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Univ Tokyo, Inst Engn Innovat, Tokyo 1138656, Japan
Japan Fine Ceram Ctr, Nanostruct Res Lab, Nagoya, Aichi 4568587, JapanUniv Tokyo, Inst Engn Innovat, Tokyo 1138656, Japan